Why does hysteresis occur? The existence of domains is a necessary condition for ferromagnetic materials to exhibit the phenomenon of hysteresis. But how are domains responsible for the phenomenon of hysteresis? What is the underlying mechanism?
 A: There is an energy associated with domain wells, which results in a kind of surface tension. In a uniform material, domain walls can move easily to respond to a change in an external field. But when there are grain boundaries, non-magnetic inclusions etcetera, domain walls will get stuck for a while. In an increasing external field this results in stick-slip motion of the domain walls, which can be made audible as Barkhausen noise. Here an animation: https://commons.wikimedia.org/wiki/File:Barkhausensprung.gif
This also results in a remanent magnetization when there is no external field. A non-zero coercive field is the needed to reverse the magnetization. The value of this coercive field can differ by many orders of magnitude for different materials.
A: In a nutshell, magnetic hysteresis exists because the relation between the applied magnetic field and the magnetization of the material is nonlinear.  If you cycle on and off the applied field there will be a remnant magnetization (i.e., alignment of domains). You have to do work to demagnetize the sample, heat or an opposing magnetic field.  Even magnetic hysteresis doesn't require ferromagnetic domains since you see in spin glasses. In liquid-solid phase transitions there are materials whose melting and freezing point are very different.  Here is a cool example from wikipedia:  "Hysteresis manifests itself in state transitions when melting temperature and freezing temperature do not agree. For example, agar melts at 85 °C and solidifies from 32 to 40 °C. This is to say that once agar is melted at 85 °C, it retains a liquid state until cooled to 40 °C. Therefore, from the temperatures of 40 to 85 °C, agar can be either solid or liquid, depending on which state it was before."
